A and B are two balloons at the same height and 1000m apart.O is ground observation position, angle AOx=45°15' and angle BOX=10°30'.find the height of the balloons

Answer 1

To find the height of the balloons, we can use trigonometry.

Let the height of balloons A and B be h meters.

From the given information, we have the following triangle:
- Triangle AOX with angle AOx = 45°15' = 45.25°, angle A = 90°
- Triangle BOX with angle BOX = 10°30' = 10.5°, angle B = 90°

Let's start by finding the distances AO and BO:

tan(AOx) = h / AO
tan(45.25°) = h / AO
AO = h / tan(45.25°)

tan(BOX) = h / BO
tan(10.5°) = h / BO
BO = h / tan(10.5°)

Given that AO + BO = 1000m, we can write:

h / tan(45.25°) + h / tan(10.5°) = 1000

Now, we can solve this equation to find the height h of the balloons:

h / tan(45.25°) + h / tan(10.5°) = 1000
h(1 / tan(45.25°) + 1 / tan(10.5°)) = 1000
h = 1000 / (1 / tan(45.25°) + 1 / tan(10.5°))

Calculating the values of tan(45.25°) and tan(10.5°) and substituting them into the equation, we get:

h = 1000 / (1 / tan(45.25°) + 1 / tan(10.5°))
h = 1000 / (1 / 0.9306 + 1 / 0.1826)
h = 1000 / (1.0741 + 5.4745)
h = 1000 / 6.5486
h ≈ 152.60 meters

Therefore, the height of the balloons is approximately 152.60 meters.